Shell script detecting errors from command called by script

I am calling applications from my shell script, which performs a number of important steps in sequence, one step being below:

for database in $( 
        echo 'show databases;' | 
        mysql --defaults-extra-file=/etc/sqlbackup/my.cnf \
              -e 'show databases' -s --skip-column-names|
        grep -vi information_schema )
do
  echo $database
done
exit 0

I am able to be able to log the output to the screen, that I am doing via the echo function.

My question is what would happen if an application (any command line called from the script), cannot connect and chucked an error such as:

`ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)`?

Are errors reported in a separate environment variable outside the string output, if so how can I detect this? How would one change the path the script takes depending on success or failure?

I am a .Net programmer and the best analogy i can make is where an exception is thrown and handeled:

catch (Exception e)
{
  // log the reason here: echo "error running database command: " + e.Description
}

Is there something similar to the above but for borne/bash shell?